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Logic and Pragmatism: Selected Essays by Giovanni VailatiCenter for the Study of Language and Inf. 2010._Logic and Pragmatism_ features a number of the key writings of Giovanni Vailati, the Italian mathematician and philosopher renowned for his work in mechanics, geometry, logic, and epistemology. The selections in this book—many of which are available here for the first time in English—focus on Vailati’s significant contributions to the field of pragmatism. Accompanying these pieces are introductory essays by the volume’s editors that outline the traits of Vailati’s pragmatism and provide insight…Read more
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27The Right Order of Concepts: Graßmann, Peano, Gödel and the Inheritance of Leibniz's Universal CharacteristicPhilosophia Scientiae 18 (1): 157-182. 2014.This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive investig…Read more
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23Il sorgere di nuove geometrie nell'Ottocento: alcune riflessioni storico-filosofiche sui fondamenti della matematicaRivista di Storia Della Filosofia 4. 1998.
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4F. Barone, Logica formale e logica trascendentale, Milano, Unicopli, 1999-2000Rivista di Storia Della Filosofia 57 (4): 701-704. 2002.
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557Is Common Ground a Word or Just a Sound?In H. V. Hanson (ed.), Proceedings of the International Conference: Dissensus & The Search for Common Ground, Ontario Society For the Study of Argumentation. pp. 1--9. 2007.The paper analyses the role played by the concept of ‘common ground’ in argumentation theories. If a common agreement on all the rules of a discursive exchange is required, either at the beginning or at the end of an argumentative practice, then no violation of the rules is possible. The paper suggests an alternative understanding of ‘common ground’ as something that can change during the development of the argumentative practice, and in particular something that can change without the practice …Read more
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Proceedings of the International Conference: Dissensus & The Search for Common GroundOntario Society for the Study of Argumentation. 2007.
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14Geometry and Measurement in Otto Hölder’s EpistemologyPhilosophia Scientiae 17 (1): 131-164. 2012.L’article a pour but d’analyser la conception de la géométrie et de la mesure présentée dans Intuition et Raisonnement [Hölder 1900], « Les axiomes de la grandeur et la théorie de la mensuration » [Hölder 1901] et La Méthode mathématique [Hölder 1924]. L’article examine les relations entre a) la démarcation introduite par Hölder entre géométrie et arithmétique à partir de la notion de ‘concept donné’, b) sa position philosophique par rapport à l’apriorisme kantien et à l’empirisme et c) le choix…Read more
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1142Aristotle’s prohibition rule on kind-crossing and the definition of mathematics as a science of quantitiesSynthese 174 (2): 225-235. 2010.The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing fo…Read more
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499Algorithms and Arguments: The Foundational Role of the ATAI-questionIn Frans H. van Eemeren, Bart Garssen, David Godden & Gordon Mitchell (eds.), Proceedings of the Seventh International Conference of the International Society for the Study of Argumentation (pp. 192-203), Rozenberg / Sic Sat. 2011.Argumentation theory underwent a significant development in the Fifties and Sixties: its revival is usually connected to Perelman's criticism of formal logic and the development of informal logic. Interestingly enough it was during this period that Artificial Intelligence was developed, which defended the following thesis (from now on referred to as the AI-thesis): human reasoning can be emulated by machines. The paper suggests a reconstruction of the opposition between formal and informal logic…Read more
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24Le concept d’espace chez VeronesePhilosophia Scientiae 13 129-149. 2009.Giuseppe Veronese (1854-1917) est connu pour ses études sur les espaces à plusieurs dimensions ; moins connus sont les écrits « philosophiques », qui concernent les fondements de la géométrie et des mathématiques et qui expliquent les raisons pour la construction d’une géométrie non-archimédienne (une dizaine d’années avant David Hilbert) et la formulation d’un concept de continu, qui contient des éléments infinis et infiniment petits. L’article esquissera quelques traits saillants de son épisté…Read more
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Geometry and geometries in the 19th century-Report on the history of mathematics conference held in Rende (Cosenza), Italy, June 29-July 3, 1998 (review)Rivista di Storia Della Filosofia 53 (4): 745-748. 1998.
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962Life and Works of Giovanni VailatiIn Cantù Paola & De Zan Mauro (eds.), Life and Works of Giovanni Vailati, Csli Publications. 2009.The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a fo…Read more
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15Richard Tieszen, After Gödel. Platonism and Rationalism in Mathematics and LogicJournal for the History of Analytical Philosophy 2 (8). 2014.Oxford: Oxford University Press 2011, x + 245 pp. £44.00 (hardcover). ISBN 978-0-19-960620-7.
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39General IntroductionPhilosophia Scientiae 17 (17-1). 2013.1 The epistemology of Otto Hölder This special issue is devoted to the philosophical ideas developed by Otto Hölder (1859-1937), a mathematician who made important contributions to analytic functions and group theory. Hölder’s substantial work on the foundations of mathematics and the general philosophical conception outlined in this work are, however, still largely unknown. Up to the present, philosophical interest in Hölder’s work has been limited to his axiomatic formulation of a theory of..
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36Benjamin Schnieder, Substanz und Adhärenz. Bolzanos Ontologie des Wirklichen, Sankt Augustin, Academia Verlag, 2002, 269 pages.Benjamin Schnieder, Substanz und Adhärenz. Bolzanos Ontologie des Wirklichen, Sankt Augustin, Academia Verlag, 2002, 269 pages (review)Philosophiques 33 (1): 306-308. 2006.
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1147Bolzano versus Kant: mathematics as a scientia universalisPhilosophical Papers Dedicated to Kevin Mulligan. 2011.The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but a…Read more
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Centre National de la Recherche ScientifiqueCentre D'Epistemologie Gilles Gaston Granger, Université Aix-MarseilleRegular Faculty
Areas of Specialization
Epistemology |
Philosophy of Mathematics |